The ICICS/CS Reading Room

UBC CS TR-89-02 Summary

The minimum degree algorithm is known as an effective scheme for identifying a fill reduced ordering for symmetric, positive definite, sparse linear systems.
Although the original algorithm has been enhanced to improve the efficiency of
its implementation, ties between minimum degree elimination candidates are still
arbitrarily broken. For many systems, the fill levels of orderings produced by the
minimum degree algorithm are very sensitive to the precise manner in which these
ties are resolved. This paper introduces several tiebreaking schemes for the minimum degree algorithm. Emphasis is placed upon a tiebreaking strategy based on
the deficiency of minimum degree elimination candidates, which can consistently
identify low fill orderings for a wide spectrum of test problems. The tiebreaking
strategies are integrated into a quotient graph form of the minimum degree algorithm with uneliminated supernodes. Implementations of the enhanced forms
of the algorithm are tested on a wide variety of sparse systems to investigate the
potential of the tiebreaking strategies.

If you have any questions or comments regarding this page please send mail to
help@cs.ubc.ca.